2024/08/02 by Ralf Hiptmair, Christoph Schwab, Hiptmair, Ralf +3
Engineering · #Acoustic Wave Phenomena Research #FOS: Mathematics #Numerical Analysis (math.NA) #Structural Health Monitoring Techniques
paper · pdf · doi:10.48550/arxiv.2408.01194
openalex publication_date 2024/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider frequency-domain acoustic scattering at a homogeneous star-shaped penetrable obstacle, whose shape is uncertain and modelled via a radial spectral parameterization with random coefficients. Using recent results on the stability of Helmholtz transmission problems with piecewise constant coefficients from [A. Moiola and E. A. Spence, Acoustic transmission problems: wavenumber-explicit bounds and resonance-free regions, Mathematical Models and Methods in Applied Sciences, 29 (2019), pp. 317-354] we obtain frequency-explicit statements on the holomorphic dependence of the scattered field and the far-field pattern on the stochastic shape parameters. This paves the way for applying general results on the efficient construction of high-dimensional surrogate models. We also take into account the effect of domain truncation by means of perfectly matched layers (PML). In addition, spatial regularity estimates which are explicit in terms of the wavenumber k permit us to quantify the impact of finite-element Galerkin discretization using high-order Lagrangian finite-element spaces.